#Physicsfactlet (88)
A charge emits radiation when accelerated, so we can apparently tell if the charge is in free fall or not, violating the equivalence principle.
Solution: the charge will still be at thermal equilibrium with the vacuum, which will look hotter (Unruh effect).
Because Maxwell's equations admit homogeneous solutions, they cannot determine a unique electromagnetic field from a given charge-current distribution until and unless suitable boundary conditions are imposed. And boundary conditions are, by definition, non-local.
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There is one charge, and the field it produces is given by the inhomogeneous solution The homogeneous one describe the fields that would be there without charges, and is therefore irrelevant to this problem.
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But there is no "the" inhomogeneous solution, and indeed there cannot be. That is the whole point. One can only distinguish between inhomogeneous solutions by the imposition of boundary conditions. This is a fundamental mathematical inevitability.
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